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- MCQs: Ch 02 Sets, Functions and Groups @fsc-part1-ptb:mcq-bank
- r HSSC-I), Punjab Text Book Board, Lahore. The answers are given at the end of the page. ====MCQs==== - A well defined collection of distinct objects is calle... or membership of a set is - $\forall$ - $\wedge$ - $<$ - $\in$ - If every element of... se - If $A$ is a subset of $B$ then $A=B$, then we say that $A$ is an - Proper subset of $B$
- Definitions: FSc Part 1 (Mathematics): PTB
- Textbook Board (PTB) Lahore, Pakistan are given. We are very thankful to **Muhammad Waqas Sulaiman** ... sent irrational number.\\ e.g. $\pi = 3.1415...$, we don’t have exact decimal representation of this n... == * **Set:** A set is generally described as a well-defined collection of distinct objects or a well-defined object collection of distinct object is ca
- Definitions: FSc Part 1 (Mathematics): PTB by Aurang Zaib
- by Punjab Textbook Board (PTB) Lahore, Pakistan. We are very thankful to [[:people:aurang-zaib]] for ... onal numbers. ===Example=== \( \pi \) (pi) is a well-known non-terminating, non-recurring decimal. I... 2: Set and Operations===== ====Set==== A set is a well-defined collection of distinct objects or eleme... , \ldots\} \), where each element is distinct and well-defined. ====Methods to describe a set==== The
- MCQs: Ch 01 Number Systems @fsc-part1-ptb:mcq-bank
- r HSSC-I), Punjab Text Book Board, Lahore. The answers are given at the end of the page. ====MCQs====... - $\displaystyle{\frac{p}{q}}$ where $p,q \in z \wedge q \neq 0$ - $\displaystyle{\frac{q}{p}}$ where $p,q \in z \wedge q \neq 0$ - $\displaystyle{\frac{p}{q}}$ where $p,q \in Z \wedge q = 0$ - $\displaystyle{\frac{q}{p}}$ wher
- Exercise 2.8 (Solutions) @fsc-part1-ptb:sol:ch02
- \ \hline 1 & 1 & 0 \\ \hline \end{array} \] Answers the questions: (i) Name the identity element i... belian? **Solutions**\\ (i) From the given table we have $0+0=0$ and $0+1=1$. This show that $0$ is ... )=(-a)+a=0$. Thus inverse of $a$ is $-a$. Hence, we conclude that set of integers form groups with re... roup. For $A\in P(S)$ where A is a subset of $S$ we have $S\in P(S)$ such that $A\cap S=S\cap A=A$.
- Ch 06: Sequences and Series @fsc-part1-ptb:important-questions
- $\frac{a^n+b^n}{a^{n-1}+b^{n-1}}$ maybe $A.M$ between $a$ and $b$. --- //BISE Gujrawala(2015)// *... odha(2015)// * If $15$ and $8$ are two A.Ms between $a$ and $b$, find $a$ and $b$. --- //BISE Sargo... //BISE Sargodha(2015)// * Find three $A.Ms$ between $3$ and $11$ --- //BISE Sargodha(2016)// * H... dha(2016),FBISE(2016)// * Insert two $G.Ms$ between $2$ and $16$ --- //BISE Sargodha(2017)// * I
- MCQs: Ch 04 Quadratic Equations @fsc-part1-ptb:mcq-bank
- r HSSC-I), Punjab Text Book Board, Lahore. The answers are given at the end of the page. ====MCQs====... - Both $A$ and $B$ - None of these - If we solve $ax^2+bx+c=0$ by complete square method, we get - Cramer's rule - De Morgan's Law -... $A$ and $B$ - None of these - The highest power of $x$ in polynomial in $x$ is called - Coef
- Multiple Choice Questions (MCQs)
- mbers is that $\forall a, b, c \in R$ * $a<b \wedge c>0\Rightarrow ac\geq bc$ * $a<b \wedge c>0\Rightarrow ac> bc$ * $a<b \wedge c>0\Rightarrow ac< bc$ * $a>b \wedge c>0\Rightarrow ac= bc$ - Which of the following is an e
- Trigonometric Formulas
- or odd. **Step II:** If $n$ is even then the answer will be in $\sin$ and if the $n$ is odd then $\s... is lying if it is in Ist or IInd quadrant the answer will be positive as sin is positive in these qua... and if it is in the IIIrd or IVth quadrant the answer will be negative.\\ e.g. $\sin {{667}^{{}^\circ ... eft( 7(90)+37 \right)$\\ Since $n=7$ is odd so answer will be in $\cos$ and 667 is in IVth quadrant an
- Ch 02: Functions and Groups @fsc-part1-ptb:important-questions
- (2,4)$ --- // BISE Gujrawala(2015)// * Find power set of $\{a,\{b,c\}\}$ --- // BISE Gujrawala(... E Gujrawala(2015)// * What is the difference between $\{a,b \}$ and $\{\{a,b\}\}$ --- // BISE Gujr... Sargodha(2015)// * Write the set $\{x|x \in Q \wedge x^2=2\}$ in descriptive and tabular form ---... // BISE Sargodha(2015)// * Write down the power set of $\{a,b,c\}$ --- // BISE Sargodha(201
- Exercise 1.2 (Solutions) @fsc-part1-ptb:sol:ch01
- <panel> **Question 13 ** Prove that the sum as well as the product of any two conjugate complex num... ext{ as } x, y \in \mathbb{R}. \end{align} Hence, we proved that sum as well as the product of any two conjugate complex number is a real number. </panel
- Definitions: Mathematics 11: PTB by Muzzammil Subhan
- by Punjab Textbook Board (PTB) Lahore, Pakistan. We are very thankful to [[:people:muzzammil-subhan]]... ction:** A function in which variable appear as power of a constant is called exponential Function. e.
- FSc Part 1 Mathematics Notes/Solutions
- ead> There are fourteen chapters in this book and we have work hard to make easy and suitable solution... . To view PDF files, there must be PDF Reader (Viewer) installed on your PC or mobile or smartphone. I
- Ch 07: Permutation, Combination and Probability @fsc-part1-ptb:important-questions
- igits $2,2,3,3,4,4$? How many of them with lie between $400,000$ and $430,000$? ---// BISE Gujrawala(... FBISE(2017)// * Show that sum of $n$ $AM's$ between $a$ and $b$ is equal to $n$ times their $AM's$
- Exercise 1.1 (Solutions) @fsc-part1-ptb:sol:ch01
- {ak}{bk}, k\neq 0\right)$ </panel> </col></grid> <well> **Book:** \\ Exercise 1.1: Textbook of Algebra... ou remix, transform, or build upon the material, you may not distribute the modified material. </well>